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The different communications of users in social networks play a key role in effect to each other. The effect is important when they can achieve their goals through different communications. Studying the effect of specific users on other users has been modeled on the influence maximization problem on social networks. To solve this problem, different algorithms have been proposed that each of which has attempted to improve the influence spread and running time than other algorithms. Due to the lack of a review of the meta-heuristic algorithms for the influence maximization problem so far, in this paper, we first perform a comprehensive categorize of the presented algorithms for this problem. Then according to the efficient results and significant progress of the meta-heuristic algorithms over the last few years, we describe the comparison, advantages, and disadvantages of these algorithms. [ABSTRACT FROM AUTHOR]